Series Definition and 998 Threads

Previously, there was a possibility that HBO would make a series, https://www.physicsforums.com/threads/hbo-will-make-asimovs-foundation.781302/ but, https://www.bbc.com/culture/article/20210920-foundation-the-unfilmable-sci-fi-epic-now-on-our-screens Filmmaker David S Goyer was working...

I don't understand what the question is asking. the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.

The speed of the block after the nth collision is $$ V_n=(2e)^n*v_0 $$ By conservation of energy the block travels a distance $$V_n^2/(2ug)$$ on the nth bounce. So the total distance is $$ d=1/(2ug)∗(v_0^2+(2ev_0)^2...) $$ $$ d=1/(2ug)∗(v_0^2/(1−4e^2)) $$ $$ d=1/(2ug)∗(v_0^2∗M^2/(M^2−4m^2))...

To determine the voltage I did voltage/number of globes: 24/16 = 1.5V per globe - Not sure if this is correct or not To determine current, I figured out using resistance formulas that the resistance for each set of 8 globes is 15 ohms R = V/I 24/3.2 = 7.5 ohms total resistance 7.5-1 = 2 * 15-1...

I have read one shouldn't plug a power strip into another power strip. Why might that be? I don't mean to exceed the number of outlets of the first strip. I just don't have enough space between outlets to plug everything in. Like a 1/2" between the outlets would be fine.

In the homework I am asked to proof this, the hint says that I can use the triangle inequality. I was thinking that if both series go to a real number, a real number is just any number on the real number line, but how do I go from there,

I have an experimantally obtained time series: n_test(t) with about 5500 data points. Now I assume that this n_test(t) should follow the following equation: n(t) = n_max - (n_max - n_start)*exp(-t/tau). How can I find the values for n_start, n_max and tau so as to find the best fit to the...

To me it seems like the formula applies to capacitors of any shape or size, since textbooks never mention any limitations on capacitor type when stating these formulae.

Greetings here is the exercice My solution was as n^2+n+1/(n+1) tends asymptotically to n then the entire stuffs inside the sinus function tends to npi which make it asymptotically equal to sin(npi) which is equal to 0 and consequently the sequence is Absolutely convergent Here is the...

Hello. I'm not sure how the generalisation comes about (where I circle). I assume that r means the the rth derivative of f(x). If that's the case, as I plug 3 = r into this generalisation, the third derivative term should equal to (-1)^3x^7 /7!, but the third derivative term is -1x^3/3...

This alternating series indentity with ascending and descending reciprocal factorials has me stumped. \frac{1}{k! \, n!} + \frac{-1}{(k+1)! \, (n-1)!} + \frac{1}{(k+2)! \, (n-2)!} \cdots \frac{(-1)^n}{(k+n)! \, (0)!} = \frac{1}{(k-1)! \, n! \, (k+n)} Or more compactly, \sum_{r=0}^{n} (...

Hi, Supposed that Raul was learning Korean, because he would like to work with BTS and BLACKPINK's agency, which requires fluency in Korean. And let's assumed that his mother tongue language is Indonesian. After several months of courses and he adequately understood Korean, he decided to watch...

I'm not sure which test is the best to use, so I just start with a divergence test ##\lim_{n \to \infty} \frac {n+3}{\sqrt{5n^2+1}}## The +3 and +1 are negligible ##\lim_{n \to \infty} \frac {n}{\sqrt{5n^2}}## So now I have ##\infty / \infty##. So it's not conclusive. Trying ratio test...

So I am having some difficulty expressing this series explicitly. I just tried finding some terms ##b_{0} = 5## I am assuming I am allowed to use that for ##b_{1}## for the series, even if the series begins at ##n=1##? With that assumption, I have ##b_{1} = -\frac {5}{4}## ##b_{2} = -...

I have found the Taylor series up to 4th derivative: $$f(x)=\frac{1}{2}-\frac{1}{4}(x-1)+\frac{1}{8}(x-1)^2-\frac{1}{16}(x-1)^3+\frac{1}{32}(x-1)^4$$ Using Taylor Inequality: ##a=1, d=2## and ##f^{4} (x)=\frac{24}{(1+x)^5}## I need to find M that satisfies ##|f^4 (x)| \leq M## From ##|x-1|...

So am trying to find the current in the RLC series circuit ,but i think i have done something wrong ,if anyone could tell me where i went wrong ,it would be great ,thank you Resistor-100ohms Capacitor-0.01uF Inductor-25mH Voltage Source-50v a.c 1kHz

Hello, I've been using "Guide to Essential Math" by S.M. Blinder from time to time to stay on top of my basic mathematics. I'm currently on the section on Bernoulli Numbers. In that section he has the following (snippet below). Is the transition to equation 7.61 just wrong? The equation just...

Hello everyone first time here. don't know if it's the correct group... Am having some issues wiz my maths homework that going to count as a final assessment. Really Really need help. The function (f), with a period of 2π is : f(x) = cosh(x-2π) if x [π;3π].. I had to do a graph as the first...

I was studying uniform convergence. I have doubts a) Prove that series $\displaystyle\sum_{n=1}^\infty{\displaystyle\frac{ln(1+nx)}{nx^n}}$ converges uniformly on the set $ S = [2, \infty) $. b Prove that series $\displaystyle\sum_{n=1}^\infty{(-1)^{n+1} \displaystyle\frac{e^{-nt}}{\sqrt[...

I looked at the solution of this problem since its a solved problem. I am having doubts with the charges relationship as is mentioned in screenshot below. The charges ##{q_3}^{'}## and ##{q_4}^{'}## are the charges after a a state of balance is reached. Why would the charges have the...

I came across the following explanation from the famous book of Sears and Zemansky which I am unable to understand. I can get the initial part where a positive charge goes to the top plate of C1 since the point a is at a +ve potential causing free electrons to transfer from top plate of C1 to...

How do I find a coefficent of x^9 in a power series like this:

Greetings according to the function we can see that there is a jump at x=e and I know that the value of the function at x=e should be the average between the value of f(x) at this points my problem is the following the limit of f(x) at x=e is -infinity and f(e)=1 how can we deal with such...

Disclaimer: Some of you might easily recognize that the components and circuit I am talking about are related to one of my projects, on which I had posted some months ago. Actually, the circuit is the same as the one in my project, but the one I am posting in this thread actually uses high...

It is clear that the terms of the sequence tend to zero when n tends to infinity (for some α) but I cannot find a method that allows me to understand for which of them the sum converges. Neither the root criterion nor that of the relationship seem to work. I tried to replace ##\sqrt[n]{n}## with...

Good day I have a question about the convergence of the following serie I understand that the racine test shows that it an goes to 2/3 which makes it convergent but I also know that for a sequence to be convergent the term an should goes to 0 but the lim(n---->inf) ((2n+100)/(3n+1))^n)=lim...

We sometimes write that \sin x=x+O(x^3) that is correct if \lim_{x \to 0}\frac{\sin x-x}{x^3} is bounded. However is it fine that to write \sin x=x+O(x^2)?

Can I create a nonlinear spring, for a nonlinear oscillator, by putting many linear springs in series and parallel?

I have a question. I’m reading the series of the practical man which include arithmetic, algebra,geometry, Trigonometry and Calculus. I’m having some trouble understanding these books and was thinking about reading the series of ____ for dummies such as Geometry for dummies as a supplement. Is...

Hello, I was wondering how to prove that the Binomial Series is not infinite when k is a non-negative integer. I really don't understand how we can prove this. Do you have any examples that can show that there is a finite number when k is a non-negative integer? Thank you!

Hi all, I have a project to code in 8051 series, DS80C320-ECG (data source as reference): "Division of two 16 bit unsigned integers being in the internal memory, quotient and remainder should be stored". I find a way to do it but there is a part of the program that i don't understand, I attach...

Hi, I have a quick question about whether or not the infinite series of 1/n converges or diverges. My textbook tells me that it diverges, but my textbook also says that by the nth term test if we take the limit from n to infinity of a series, if the limit value is not equal to zero the series...

Would someone be able to explain like I am five years old, what is the precise relationship between Fourier series and Fourier transform? Could someone maybe offer a concrete example that clearly illustrates the relationship between the two? I found an old thread that discusses this, but I...

Hello ! Consider this series; $$ \sum_{k=1}^{\infty} \frac{1}{(2k-1)(2k+1)} $$ It is said to find the limit of the series when approaches infinity.Now it is said that this is a telescopic series and that the limit is ##\frac{1}{2}## but I don't see it. I've split the an part (I don't know how...

Summary:: I am suspossed to find the limit of this series.I've come to realize that the series diverges and I'm trying to prove that using the a comparison test. Hello! Consider this sum $$ \sum_{k=1}^{n} (\sqrt{1+k} - \sqrt{k}) $$ the question wants me to find the limit of this sum where n...

I have two capacitors in series across my bus. I have a some series resistors across the capacitors for voltage balancing. I would like to power some low voltage low voltage components tapping off of the voltage divider using that as the voltage supply. The bus voltage will be approximately 2...

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Summary:: About resonant frequencies A series RLC circuit with R = 250 ohms and L = 0.6 H results in a leading phase angle of 60° at a frequency of 40 Hz. At what frequency will the circuit resonate? Answer is 81.2 Hz but i got a different answer. May someone please correct me.

Good afternoon all, On page 51 of David Griffith's 'Introduction to Quantum Mechanics', 2nd ed., there's a discussion involving the alternate method to getting at the energy levels of the harmonic oscillator. I'm filling in all the steps between the equations on my own, and I have a question...

I want to check my calculations via mathematica. In the book I am reading there's this expansion: $$\frac{(1+\frac{1}{j})^x}{1+x/j}=1+\frac{x(x-1)}{2j^2}+\mathcal{O}(1/j^3)$$ though I get instead of the term ##\frac{x(x-1)}{2j^2}## in the rhs the term: ##-\frac{x(x+1)}{2j^2}##. So I want to...

We usually talk about ##F[[x]]##, the set of formal power series with coefficients in ##F##, as a topological ring. But we can also view it as a topological vector space over ##F## where ##F## is endowed with the discrete topology. And viewed in this way, ##\{x^n:n\in\mathbb{N}\}## is a...

I've calculated the change in the entropy of material after it comes in contact with the reservoir: $$\Delta S_1 = C \int_{T_i+t\Delta T}^{T_i+(t+1)\Delta T} \frac{dT}{T} = C \ln{\frac{T_i+(t+1)\Delta T}{T_i+t\Delta T}}$$ Now I would like to calculate the change in the entropy of the...

Hello, this is my working. My professor did not give any answer key, and thus can I check if I approach the question correctly, and also check if my answer is correct at the same time. for t < 0, V(0-) = V(0+) = 60V I(0) = 60 / 50 = 1.2A When t > 0, $$α = \frac{R}{2L}$$ $$α =...

I calculated in the following and got the correct answer. However, I wonder whether this way is correct or not. Thanks! PR / Pavg = Irms^2 * R / Irms^2*Z = 15 /33.36 = 0.45

I'm a bit confused with RLC circuit. If in series, IL = IL, max * cos(wt) If in parallel, IL = - IL, max * cos(wt) Are these correct?

Good day I really don't understand how they got this result? for me the sum of the Fourier serie of of f is equal to f(2)=log(3) any help would be highly appreciated! thanks in advance!

I wonder if the limit of the following can be converted into integral or some elegant form as N tends to infinity: \[ \sum_{n=0}^{N}\frac{a}{2^{n}}\sin^{2}\left(\frac{a}{2^{n}}\right) \] If we plot or evaluate the value then it does appear that the series converges very fast...

I was recently studying the pressure gradient force, and I found it interesting (though this may be incorrect) that you can use a Taylor expansion to pretend that the value of the internal pressure of the fluid does not matter at all, because the internal pressure forces that are a part of the...

Good day I'm trying to find the radius of this serie, and here is the solution I just have problem understanding why 2^(n/2) is little o of 3^(n/3) ? many thanks in advance Best regards!